1. Field of the Invention
The present invention relates generally to methods and systems of quantifying uniformity of measure quantities on semiconductor wafers, and more particularly, to improved methods and systems for quantifying nonuniformity patterns on semiconductor wafers before during and after process operations.
2. Description of the Related Art
Semiconductor wafers undergo numerous processes during the semiconductor manufacturing process. Layers may be added, patterned, etched, removed, polished and many other processes. After each process the wafer is typically examined to confirm the previous process was completed with an acceptable level of errors or nonuniformities. The various operating variables (e.g., event timing, gas pressure, concentrations, temperatures, etc.) of each process the wafer is processed through are recorded so that any changes in any variable may be quickly identified and potentially correlated to any errors or nonuniformities discovered when the wafer is examined
FIG. 1A shows a typical etched wafer 100. A top layer of material was mostly removed from the wafer in the etch process except for a portion 106 of the top layer. For clarity purposes, the portion 106 is a portion of a layer or ultrathin film. A notch 104 is typically included in each wafer 100 so that the wafer can be oriented (aligned) in the same position during the various manufacturing processes. The portion 106 is a nonuniform portion of the surface of the wafer 100 and therefore can be termed a nonuniformity. As shown, the portion 106 is in the approximate form of a ring or annular shape where the top layer was removed from the center and around the edges of the wafer 100.
FIG. 1B shows another typical etched wafer 120. A portion 108 of a top layer remains, when the top layer was mostly removed in the etch process. The portion 108 is typically termed an azimuthal-type nonuniformity on the surface of wafer 120 because the nonuniformity 108 is not the same at the same radius around the wafer 120.
Prior art approaches to describing nonuniformities 106, 108 include subjective, verbal descriptions such as “center-fast” for annular nonuniformity 106 or “left side slow” for azimuthal nonuniformity 108. Center-fast generally describes wafer 100 because material from the center of the wafer 100 is removed faster than the material in the annular region 106. However, center-fast does not provide a specific, objective and quantitative description of the nonuniformity 106. Similarly, left side slow describes wafer 120 because the etch process removed material from the left side region 108 slower than the other regions of the wafer 120 but left side slow also fails to provide a specific, objective and quantitative description of the nonuniformity 108.
The descriptions of the nonuniformities 106, 108 are used to provide feedback to correct errors and inconsistencies in the etch and other preceding processes that were performed on the wafers 100, 120. The descriptions of the nonuniformities 106, 108 can also be used to track the impact of the nonuniformities 106, 108 on subsequent semiconductor manufacturing process and on metrics from completed semiconductor devices (e.g., device yields, performance parameters, etc.)
As nonuniformities become smaller and smaller, the nonuniformities become less symmetrical and also more difficult to accurately describe with the subjective, verbal descriptions. FIG. 1C shows a typical wafer 150 with multiple, asymmetrical nonuniformities 152A-G. The nonuniformities 152A-G can be smaller and are less symmetrical than nonuniformities 106, 108 because the various variables in the etch and other previous processes are very stringently controlled. The subjective, verbal descriptions have therefore become insufficient to accurately describe the nonuniformities 152A-G so that further improvements in the preceding processes can be successfully completed.
A more objective description of wafer uniformity is referred to as a 3-sigma uniformity metric. The 3-sigma uniformity metric quantifies a standard deviation of measurements of some quantity of the wafer. By way of example, the 3-sigma can be an expression of the deviations in thickness of the wafer detected by an array of measurement points across the wafer. FIG. 1D shows a typical 49-point array used in completing a measurement scan of wafer 160. The thickness of the wafer 160 is measured at each of the 49 points. The 49-points are arranged with a center point 162, and three concentric rings 164, 168, 172. The inner ring 164 has 8 evenly spaced points. The intermediate ring 168 has 16 evenly spaced points. The outer ring 172 has 24 evenly spaced points. The rings 164, 168, 172 are typically approximately equally spaced radially from the center point 162. Each of the points in the rings 164, 168, 172 and the center point 162 is typically assigned to represent a given portion of the wafer 160. For example, a typical wafer 160 has a 3 mm exclusion zone on the outer perimeter of the wafer 160. The rings 164, 168, 172 and the center point 162 are spaced equidistant and therefore each of the 49 points represent about {fraction (1/49)}th of the area of the wafer 160, less the 3 mm exclusion zone (i.e., the outer edge of the wafer where expected process abnormalities occur). Because nonuniformities do not suddenly appear under a single scan point, the nonuniformities are smoothed due to the choice of measuring points.
The 3-sigma uniformity metric is conventionally defined to be equal to 3 times the standard deviation of the measurements on the wafer 160. The standard deviation of the thickness of the wafer 160 is determined by a sum of the thickness of the wafer 160 at each of the 49 scanned points divided by 49 times the mean thickness of the wafer. A typical 3-sigma metric of a wafer is reported as a percentage of uniformity (0% being ideal). The 3-sigma metric is also often referred to as the WIWNU metric (within wafer nonuniformity).
A 3-sigma metric provides a single, objective, quantitative, summary description of the magnitude of the nonuniformities 152A-G. Additional metrics include skewness and kurtosis, which can be derived from the measured array data. However, these metrics do not provide sufficient information to specifically identify the location and shape of the nonuniformities on the wafer 160.
In view of the foregoing, there is a need for an improved system and method of objectively quantifying nonuniformities on a semiconductor wafer that also provides location and shape of the nonuniformities.